the radical rational…

in search of innovative ideas with a well-balanced approach for the math classroom

@Plickers #tmc14 #myfav

An APP I downloaded early in the summer, then forgot about it until dinner Friday night.  Something was said which triggered a thought, so I pulled out my phone to share with my #tmc14 roomies. Click here for more info.


I was already scheduled for a #myfav Saturday a.m. so why not introduce this fun app to others?!?

I used the hotel’s business desk to print my paper clickers, set up my account and ran back upstairs to practice. 

A QR code of sorts.  Each plicker has a number you can assign to students.  The answer you wish to submit should be at top of your page when scanning.

We scanned reponses.  Changed answers by rotating our plicker. We saved, opened and cleared responses.  It tagged the reponses w time and date.


You could see response distribution immediately.  It even listed each student’s response individually.

We were using the 5.5 inch plickers (you can print a larfer size, too) and my  device read them at 20ish feet away.

As folks arrived the next morning, I passed out plickers and asked them if they minded helping me later. 

I shared my story, asked them to hold their plickers for response A just to ensure I didn’t need to calibrate.  I scanned the room.

Based on reading tweets later, it was described as mind-blowing, #amazeballs and some other gasping descriptions too embarrassing to share.

I asked a couple of them to change their answers.  Scanned again. Yep.  They worked again. 


Smiles. Ooooo’s and Ahhhs.  It was a good thing.

Since #myfav, several have shared ideas for their claases.

Printed on cardstock. 
Students keep in INB pocket.
Color coded for each class. Student’s name on outer edge.
Single set laminated, velcro dots to attach to desks for quick access.
Laminated to back of INB.
Others I know I missed.

iOS or android.
40 different codes for larger classes.
One device.
Lose a plicker, print a new one.
Immediate feedback can sync with online account to display results.

What’s not to love?

Now to find out where I can get one of those cool t-shirts someone tweeted about!

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Walking a Z-score #tmc14

I was super excited about spending time with experienced Statistics teachers this past week at #TMC14.  On our first day together, we discussed, well, I listened mostly, what big ideas students seemed to struggle with.  A couple of teachers shared that their students could compute a z-score, but for whatever reasons, this past year, they had trouble explaining what the score actually meant.

My thought is to use something similar to  students plotting points on a number line.  Suggestions are welcomed.

String/yarn 2 colors, one shorter, the other at least 6 times its length.
Ziploc bag

Inside each bag I will include mean score, and standard deviation on an index card along with a list of data values from that sample,  a string length to model 1 standard deviation, another string length for our axis. 

Students will layout their “graph” with a longer string as the axis, taping the ends down.   What I heard others saying was that students wanted to report a probability for the z-score.  My initial thoughts are to keep it 1 dimensional and maybe alleviate this misconception.

They will place a post-it for the mean value label on the graph, use the standard deviation string to label data values occuring at each sd on the graph.

Next, they will locate the other data values on the number line and place a post-it.  I will ask them to come up with a measure of each data point using the sd string as their unit of measure.  Some discussion about what their estimates represent and my hopes that after plotting and sharing, someone will develop the z-score on their own.

Next, they will practice calculating z-scores and add to the data post-its.  They will choose one of the z-score post-its.  Next they will stand at the mean and estimate the location of their data value by “walking” on the number line, using the standard deviation string as their measurement device.  If everyone in the group agrees with the locations, the post-it note is placed on the graph.

The next team member repeats the process with another data value and so on until all z-scores have been placed.


Snap picture of each groups model.  Share out with class.  Discussions as needed. 

Quick-write reflection as the exit ticket for the day.

Just getting some ideas down, definitely some revisions to come.

I am new to statistics, so I value any feedback from seasoned teachers. 

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#tmc14 My Favorites

Chalk Talk, Making Thinking Visible
Intro to Thinking Routines



Black Lights and Highlighters



Ghosts in the Graveyard, Kim Hughey, Math Tales from the Spring

Grudge, Nathan Kraft’s I Shall Never Play a Review Game Again
Used most Fridays, either first or last 10-15 minutes of class to highlight our big ideas/skills from the week.

Plickers all you need is paper and a smart phone. New app for me, so I am still learning. What little we’ve played around, it has some great potential!

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The Moving Walkway #julychallenge Post 19

As I am walking through the airport this morning, it was not crowded and had I been brave, I would have collected some data to enable me to create a nice little work-rate problem.

How much time does that moving walkway actually save me?

Scenario 1: walk the distance.
Scenario 2: ride the distance
Scenario 3: walk while riding
Hmmm…Scenario 4: while riding, walk against the moving walkway.

The next time I have an early flight, when it’s not crowded.  You bet I will be recording some times.

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Gum Container Repurposed Dice #julychallenge Post 18

Quickest post ever!

Got these dice at a Five Below store last summer.


Ice Breakers, Ice Cubes Gum container…perfect for storing!

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Setting Personal Social-emotional Goals pt. 2 #julychallenge Post #17

This morning as I responded to a commented from @bpagirls on my post about an Essential Questions Board, a thought hit me, so I typed it in my reply so I wouldn’t forget…

… I have just realized as I type, why not add a spot for personal-social goal-setting on my organizer for each student to set, write and reflect.

It stems back to this post and one of the 14 ways to think about good teaching post, 3. Include social-emotional learning goals as well as academic goals.

I got that I needed to do this, but I was not quite sure how to set and record these goals.  My plans are to include a place on the back of our unit organizer students receive at the beginning of each unit.  These are formatted in a booklet style to fit our INBs.  Students can set a personal/social goal to focus on for the duration of the unit. Ideally, following the SMART goal format.  Commit to it by writing it on their organizer.  I will ask to see it, but they may choose whether to share with a peer.  Wouldn’t it be great to have accountability partners for the unit? 

Throughout the unit or even at beginning of class, ask them to read it to themselves.  Maybe even allow someone to share their progress.  Revisit them as we end the unit and write a brief reflection:  How did I do?  Did I meet my goal?  If not, did I at least move toward it? What do I need to modify?  Follow the format: 2 stars and a wish for their quick-write reflection.  Celebrate their progress, maybe through our Shout-Out Board (more on that later).

I realize this type of goal setting may be tough for students… I am hoping after completing this task, it will allow for students to generate ideas.

Initially, I think goals can range from:
Improved / good attendance
Be to class on time
Being prepared for class
Completion of assignments
Asking for help
Asking questions or participating in class discussions.
Attend tutoring if needed
Work in a group with people I don’t know.
Share my ideas in class
Share my assessments and progress with parents/guardian
Choose better practice/study options
Listen to others ideas
Evaluate how my choices are impacting my learning.

Here is a sample of the back of my unit organizer.  I plan to insert personal goals below the unit reflection.  Here is an updated version of a complete unit organizer and student assessment tracker. Feel free to modify for use in your personal classroom. Thanks to Crazy Math Teacher Lady and Math = Love for inspiring through their posts?


My next task is to locate a fill-in the blank for a SMART to include on the first unit.  Kind of a madlibs style to get us started.

If you have a system in place or use LIM or AVID in your school, I welcome input and suggestions.

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Essential Questions for my Walls #julychallenge Post 16

4.  Translate learning goals into meaningful, interesting questions and challenges.

What if we thought about our teaching in terms of exploring open-ended questions that are interesting and meaningful to our students? What if we put “essential” questions on the board at the beginning of units and lessons, discussed with our students why they are important and meaningful, and then referred to them throughout the unit?

Is an excerpt from this post.  Along with posts from Anna and Kate, I know this is an area of needed growth in my planning.

For several days, I’ve been bugged by the lack of interesting bulletin boards in my classroom.  It bothers me that I am satisfied with sticking a motivational poster or favorite quote up for the entire year. I want something interactive, that has potential to impact student learning. 

Apparently my frustration in a tweet got into @druinok’s mind as well.  There have been some good discussions and even great ideas as a result of her post, yet it didn’t seem to be what I was looking for.

The excerpt above was it!  Why not have an essential questions board?  As we begin a unit, post to share our EQs, offer post-its for students to add to the board as we progress, revisit throughout the unit and again as a springboard for reflection as we end.

I believe this is one idea that will meet all of my goals.  It also supports a thinking environment from this #makthinkvis post.  I am looking forward to sharing more on the progression of this idea.


Social-Emotional Learning Goals #julychallenge Post 15

Still addressing 14 ways of thinking about good teaching from this post…

3.     Include social-emotional learning goals as well as academic goals.

It can be easy as a teacher to get wrapped up in student assessment data.  We must continually keep focused on the whole-student.  I always enjoy reading @druinok’s post on her experiences with AVID- Advancement Via Individual Determination.  To my understanding, it provides students with a system that will enable them to achieve more, be aware of choices and resources and work toward their post-secondary goals.  It provides them with academic structures as well as a mentor for accountability.

Many years ago, when I first began teaching in our freshman wing, The DOCK, our goal was to instill self-Discipline,  Organizational skills, develop positive Character traits and enhance student Knowledge through learning.  Our first few years were a huge success, but I never understood why it didn’t continue throughout the remainder of the school. Being out of the DOCK now, I terribly miss our weekly meetings to discuss options and strategies for struggling students, both discliplinary and acsdemically. 

After talking with some colleagues, their view of the DOCK had been tainted by comments others had made.  This made me sad because at the very heart of our collaboration was caring for students-the whole student.  Since I am no longer with that team, I must find ways to continue those positive practices.

I began using the INBs as a measure for helping students stay organized, developing reflection and study tools that can carry through their education.  I learned about Cornell notes through @druinok’s blog and shared the idea with some colleagues.  I value what CN can do in helping students learn and achieve.  I have observed students owning their INBs which leads to better effort in class and studying.

We also used excerpts from Covey’s 7 Habits for Highly Effective Teens book to drive our charachter models.  Each month, we would do an activity and focus on a trait specific to a given habit.  This summer, our school has participated in a 3-day Leadership training, focused on the 7 habits.  Our GRIT team has been meeting weekly to plan and outline school wide activities based on our shared goals.  I see this as a positive thing for our school culture and the possibility of having major impact on students as well.

Recently, I have noticed employee tshirts, one at a restaurant, “I love my job!” on the back and at a grocery with “Glad you’re here!” on the front.  Along with a poster “You are important!” – all of these may go without saying, but why not voice them?  I am a firm believer that my attitude rubs off on the students. 


Its fun to treat them as well.  I brought caramel apple suckers to an entire class one time because a student had been there for an entire week.  What happened next? The class began encouraging her too and the was a marked turnaround in her attendance and effort the second semester. 

Some ways I plan to make this happen:
Taking notice when they are at school.
Letting them know they were missed when they were absent.
An email or phone call to parents to pat them on the back. (Five on Friday)
Meet them at the door, good morning and a smile.
High fiving a small achievement. 
A note on the back of a paper to tell them I am proud of them. 
None of those things cost a dime. 

By holding them accountable, having conversations with them individually about their progress and effort or lack of, they become more aware of the impact of their actions.  Showing them their benchmarks and having a discussion about what they can do to improve.  Then letting them write their own goal and 2 things they plan to do to meet that goal.
But don’t stop there.  Revisit their goal often to remind them, keep them on track.  Most importantly, celebrate those small successes toward the end goal can be powerful motivation.

What are some ways you enhance the social-emotional growth of your students?


My Experience with Counting Circles #julychallenge Post 14

Still addressing 14 ways of thinking about good teaching from this post

2.  Plan goals for both the long term and the short term.

My number 1 goal is to help students grow – personally and academically.  My wish is that they leave my classroom believing in themselves, more self-confident than when they entered. 

Ideally, I do want every student to reach proficiency, but I am also a realist.  When students come to me with *ACT-PLAN scores in the 10-14 range, proficiency is not an immediate goal…growth is, pure and simple.  My class becomes the stepping stone to reach proficiency.  Students in this range generally have major gaps in number reasoning.  They are just now beginning to develop understanding and knowledge of assessed skills.

Last year, I wanted to use accessible tasks to begin each day…Counting Circles, Number Talks (pg 4 of link) and my post, Estimation180, and Visual Patterns were staples in my Algebra 2 classes.  Students in these classes ranging from ACTPLAN scores from 10 to 23-wide range of abilities and varied confidence levels.  These tasks were approachable for all students and I feel helped in developing number sense which allowed several students to make significant gains on thier ACT.

Counting Circles (Thanks to Sadie!) was very popular in both classes.  We literally got out of our desks to create a “circle” around the room. Yes, it seemed trivial at first, but I was able to see student confidence grow as they strengthened numeracy skills.


My Routine
We have a starting number and a number to count by.  In the beginning, I choose nice numbers, then some that required a little more thought.  Eventually, I allow students choose our counting number and starting point.  I would have expected them to take the easy route.  Not at all.  They like to challenge themselves.  We also countdown.  I like to write their responses on the board for them to visually see the patterns.  When a student makes a mistake, I try to not point it out, but rather, allow students to have opportunity to voice their concerns with a response, respectfully, of course.

After going so far around the circle, I stop and ask, What will _______ (a little further around the circle) say next? 

We usually get a couple of responses, so I allow them to explain their process then, as a class, they determine which one makes more sense.

Also, I like to ask…who will say ______ ?

Side note: Later in a functions unit, while looking at finite differences, a student explained, this is similar to what we were doing with Counting Circle the other day!

Our First Counting Circle – Count by 10
I began with couting by 10 on decade numbers, by -10 on decade numbers, then on numbers like 11 or 14, counting by 10 in both directions.  It was a great way to model the routine.  Students are comfortable with it.

Next week, we counted by 2s, up and down, starting on positive and then a negative.

Several students are all in – they’ve got this!

Then by 5s.  On 15, 70, -85 then numbers not ending in 0 or 5…. 37, 128, -89. Both up and down.

I began using single digit integers then a few double digits.

Next week we worked with decimals +3.7,  starting with an integer, then moving to devimals 11.2.  One student this particular day was quickly running through their numbers.  When I asked their strategy, they responded….its easy, add 4 then count .1 back 3 times.

We also use fraction expressions as well.

I already know my stronger numeracy students-those with “high status” in class (Ilana Horn).  So do their classmates.  What I love about counting circles is choosing different students to explain.  Struggling students pick up on numeracy techniques as explained by their peers.  They are able to see those high-status students’ thinking and realize, “I can do that too.”  Its a win-win.

Yes, at high school age, I have students who don’t want to participate, but with a bit of coaxing, they come around. It becomes a game.  Classmates encourage those who struggle.  We don’t laugh or make fun.  They celebrate when ‘that’ student experiences success.  Most of all, they smile.

Generally, it takes anywhere from 5-15 minutes depending on number choices, discussions, size of class, experience with the routine.

Suggestions:  pre-cal count around unit circle, elementary use money as a context, what others can you share?

Long term goals and planning changes with each group of students.  Having access to learning routines like these allow me to tailor toward each groups’ needs.

*In Kentucky, every student takes the PLAN during sophomore year and ACT during their junior year as part of our state accountability model.  To measure student growth from state data, students are grouped by their PLAN scores, then compared to others in this scoring band.  Once the ACT scores are available, they are given a percentile rank from within that initial grouping.  I, the teacher, can view this and whether they had high growth, expected growth or below expected growth.  The state assigns me an overall rating and this will eventually become 20% of our Certified Evaluation plan.  The other 80% is determined locally and by student growth and proficiency goals I personally set for my students early in the school year.


Time Capsule Teaching #tbtblog #julychallenge Post 13

This tweet made me wonder….


If I created a timecapsule of my teaching strategies…what would I think when I opened it? 

I read the post, Time-Capsule Teaching and within a few moments I thought…what was I blogging about 3 years ago?  I searched back and thought I hadn’t actually started yet, but there it was…

July 17, 2011

I was new to the blogosphere. 
This was my 2nd post.
TMC did not exist yet.
I was learning about standards based grading.

After much reading and discussion with close colleagues and many hours of processing what I had read, I knew SBG would be more effective in communicating student learning.  My grades prior to this had been filled with fluff, things unrelated to actual student learning…the reason some students had good grades but were not achieving at the same level.  Initially, that’s why I started blogging was to record my journey through sbg.

2 Years ago
July 16, 2012 #made4math Monday

It was the 3rd week of #made4math.
These lovely pencils for my classroom.


I did this again last school year. 15 pencils almost lasted until Christmas break.  All in all, I put out fewer than 36 pencils for the entire year.  My daughter helps decorate-cheap flowers, pipe cleaners, feathers-whatever she finds in the craftbox to make them obnoxious.  Students no longer ask me, they just borrow.  It is easier than me taking time out of whatever task I am on to hunt them a pencil. I have a mini clipboard, students signed their name and crossed it off when they returned.  Obviously, some were not returned but that’s about 1 pencil per week.  Its worth it to me, fewer interuptions, I don’t get frustrated if the same ones are borrowing a pencil everyday. :)

The same post I shared this handy paperclip box that I just filled with paper clips before APSI last month!


1 year ago
July 23, 2013
A Reflection Tool for PLCs from @TJterryjo “I have a dream…”


Basically her PLC was asked what characteristics a dream math student would have (in green).  Then, as teachers, what they could do to create that dream (in blue).  At each PLC, they “dotified” what they had seen in students and themselves to see if they were moving toward that dream.

This is something I wanted to do but let it go.  This is on my to-to list for our first departmental PLC this school year!

Join in!
Pick a year. Any year.  Read a post and reflect…
Not been blogging that long? Pick a favorite blogger and read one of their posts from 3 years ago…
Throw-back Thursday Blog #tbtblog

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